Some Properties For Solutions To Elliptic Equations

There are two topics in this paper. The first one is about the anisotropic obstacle problem for the A-harmonic equationAn integrability result is given under suitable assumptions, which shows that higher integrability of the boundary datum and the obstacle force solutions u to have higher integrability as well, or Divergence type nonhomogeneous elliptic equation of higher order integrability.The second one is about weak monotonicity for solutions to the anisotropic elliptic equation (*), we assume anisotropic growth:there exist a measurable function α(x) and a constant β such that and Weak monotonicity property is obtained.